检索结果-南通市图书馆

A New Proof for Congruent Number’s Problem via Pythagorician Divisors

Advances in Pure Mathematics 2024年第4期14卷 283-302页

作者： Léopold Dèkpassi Keuméan fra.çois emmanuel tanoé UFR Mathematics and Computer Science F&#233lix Houphou&#235t Boigny University Abidjan Cote d&#8217Ivoire

Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets ( a,b,c )∈ ℕ 3∗ , we give a new proof of the well-known problem of these particular squareless numbers n∈ ℕ ∗ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ( A α ) 2 + ( B β ) 2 = ( C γ ) 2 , such that its area Δ= 1 2 A α B β =n;or in an equivalent way, to that of the existence of numbers U 2 , V 2 , W 2 ∈ ℚ 2∗ that are in an arithmetic progression of reason n;Problem equivalent to the existence of: ( a,b,c )∈ ℕ 3∗ prime in pairs, and f∈ ℕ ∗ , such that: ( a−b 2f ) 2 , ( c 2f ) 2 , ( a+b 2f ) 2 are in an arithmetic progression of reason n;And this problem is also equivalent to that of the existence of a non-trivial primitive integer right-angled triangle: a 2 + b 2 = c 2 , such that its area Δ= 1 2 ab=n f 2 , where f∈ ℕ ∗ , and this last equation can be written as follows, when using Pythagorician divisors: (1) Δ= 1 2 ab= 2 S−1 d e ¯ ( d+ 2 S−1 e ¯ )( d+ 2 S e ¯ )=n f 2;Where ( d, e ¯ )∈ ( 2ℕ+1 ) 2 such that gcd( d, e ¯ )=1 and S∈ ℕ ∗ , where 2 S−1 , d, e ¯ , d+ 2 S−1 e ¯ , d+ 2 S e ¯ , are pairwise prime quantities (these parameters are coming from Pythagorician divisors). When n=1 , it is the case of the famous impossible problem of the integer right-angled triangle area to be a square, solved by Fermat at his time, by his famous method of infinite descent. We propose in this article a new direct proof for the numbers n=1 (resp. n=2 ) to be non-congruent numbers, based on an particular induction method of resolution of Equation (1) (note that this method is efficient too for general case of prime numbers n=p≡a ( ( mod8 ) , gcd( a,8 )=1 ). To prove it, we use a classical proof by induction on k , that shows the non-solvability property of any of the following systems ( t=0 , corresponding to case n=1 (resp. t=1 , corresponding to case n=2 )): ( Ξ t,k ){ X 2 + 2 t ( 2 k Y ) 2 = Z 2 X 2 + 2

关键词： Prime Numbers-Diophantine Equations of Degree 2 & 4 Factorization Greater Common Divisor Pythagoras Equation Pythagorician Triplets Congruent Numbers Inductive Demonstration Method Infinite Descent BSD Conjecture

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Fermat and Pythagoras Divisors for a New Explicit Proof of Fermat’s Theorem:a⁴ + b⁴ = c⁴. Part I

引用

Advances in Pure Mathematics 2024年第4期14卷 303-319页

作者： Prosper Kouadio Kimou fra.çois emmanuel tanoé Kouassi Vincent Kouakou Laboratoire d’ Informatique et de Math&#233matiques appliqu&#233es Institut Polytechnique F&#233lix Houphou&#235t BOIGNY Yamoussoukro Cote d&#8217Ivoire UFR Mathé matiques et Informatique Universit&#233 F&#233lix Houphouet BOIGNY Abidjan Cote d&#8217Ivoire UFR Sciences Fondamentales Appliqué es Universit&#233 NANGUI ABROGOUA Abidjan Cote d&#8217Ivoire

In this paper we prove in a new way, the well known result, that Fermat’s equation a4 + b4 = c4, is not solvable in ℕ , when abc≠0 . To show this result, it suffices to prove that: ( F 0 ): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is not solvable in ℕ , (where a 1 , b 1 , c 1 ∈2ℕ+1 , pairwise primes, with necessarly 2≤s∈ℕ ). The key idea of our proof is to show that if (F0) holds, then there exist α 2 , β 2 , γ 2 ∈2ℕ+1 , such that ( F 1 ): α 2 4 + ( 2 s−1 β 2 ) 4 = γ 2 4 , holds too. From where, one conclude that it is not possible, because if we choose the quantity 2 ≤ s, as minimal in value among all the solutions of ( F 0 ) , then ( α 2 ,2 s−1 β 2 , γ 2 ) is also a solution of Fermat’s type, but with 2≤s−10) is solvable in ( a 1 ,2 s b 1 , c 1 ) , s ≥ 2 like above;afterwards, proceeding with “Pythagorician divisors”, we creat the notions of “Fermat’s b-absolute divisors”: ( d b , d ′ b ) which it uses hereafter. Then to conclude our proof, we establish the following main theorem: there is an equivalence between (i) and (ii): (i) (F0): a 1 4 + ( 2 s b 1 ) 4 = c 1 4 , is solvable in ℕ , with 2≤s∈ℕ , ( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs. (ii) ∃( a 1 , b 1 , c 1 )∈ ( 2ℕ+1 ) 3 , coprime in pairs, for wich: ∃( b ′ 2 , b 2 , b ″ 2 )∈ ( 2ℕ+1 ) 3 coprime in pairs, and 2≤s∈ℕ , checking b 1 = b ′ 2 b 2 b ″ 2 , and such that for notations: S=s−λ( s−1 ) , with λ∈{ 0,1 } defined by c 1 − a 1 2 ≡λ( mod2 ) , d b =gcd( 2 s b 1 , c 1 − a 1 )= 2 S b 2 and d ′ b = 2 s−S b ′ 2 = 2 s B 2 d b , where ( 2 s B 2 ) 2 =gcd( b 1 2 , c 1 2 − a 1 2 ) , the following system is checked: { c 1 − a 1 = d b 4 2 2+λ = 2 2−λ ( 2 S−1 b 2 ) 4 c 1 + a 1 = 2 1+λ d ′ b 4 = 2 1+λ ( 2 s−S b ′ 2 ) 4 c 1 2 + a 1 2 =2 b ″ 2 4;and this system implies: ( b 1−λ,2 4 ) 2 + ( 2 4s−3 b λ,2 4 ) 2 = ( b ″ 2 2 ) 2;where: ( b 1−λ,2 , b λ,2 , b ″ 2 )={ ( b ′ 2 , b 2 , b ″ 2 ) if λ=

关键词： Factorisation in ℤ Greatest Common Divisor Pythagoras Equation Pythagorician Triplets Fermat's Equations Pythagorician Divisors Fermat's Divisors Diophantine Equations of Degree 2 4-Integral Closure of ℤ in ℚ

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

New Asymptotic Results on Fermat-Wiles Theorem

引用

Advances in Pure Mathematics 2024年第6期14卷 421-441页

作者： Kimou Kouadio Prosper Kouakou Kouassi Vincent tanoé fra.çois UMRI MSN Felix Houphouet-Boigny National Polytechnic Institute Yamoussoukro Ivory Coast Nangui Abrogoua University Applied Fundamental Sciences Department Abidjan Ivory Coast UFRMI Flix Houphout-Boigny University Abidjan Ivory Coast

We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.

关键词： Fermat’s Last Theorem Fermat-Wiles Theorem Kimou’s Divisors Diophantine Quotient Diophantine Remainders Balzano Weierstrass Analysis Theorem

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Long-wave instabilities

引用

Science China Mathematics 2024年第8期67卷 1761-1776页

作者： Dongfen Bian emmanuel Grenier School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China Unité de Mathématiques Pures et Appliquées CNRS UMR 5669Ecole Normale Supérieure de LyonLyon 69007France

This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld equation and to detail the analysis of its *** these analyses,we prove the existence of long-wave instabilities in the cases of slowly rotating fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.

关键词： Navier-Stokes equations boundary layers Prandtl equations

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Exploring factors of disaster preparedness in UNESCO-designated heritage sites

引用

Geography and Sustainability 2024年第3期5卷 392-404页

作者： emmanuel Eze Alexander Siegmund Institute of Geography&Heidelberg Center for the Environment(HCE) University of HeidelbergHeidelbergGermany Department of Geography-Research Group for Earth Observation(r geo) UNESCO Chair on Observation and Education of World Heritage&Biosphere ReserveHeidelberg University of EducationHeidelbergGermany Geographical and Environmental Education Unit Department of Social Science EducationUniversity of NigeriaNsukkaNigeria

Increased hazards threatening the United Nations Educational,Scientific and Cultural Organization(UNESCO)-designated sites and endangering cultural heritage and community well-being require attention and ***-sidering the pivotal role of UNESCO sites in conservation and development,this study assessed their levels of disaster *** absence of studies assessing disaster awareness,risk perception,and preparedness among UNESCO site actors,as well as the pivotal place of preparedness within the Disaster Risk Management(DRM)cycle justifies this *** the tenets of the Person-Relative-to-Event fra.ework,we hypothe-sized that a strong positive correlation exists between perceived risks,resources,and disaster *** collect pertinent data,we employed an embedded mixed-method design and conducted an online questionnaire survey yielding 141 responses from 59 *** the results of relevant analyses,wildfires,floods,and droughts are top hazards occurring frequently in UNESCO sites,with significant concerns about pollution and habitat loss during future *** emerged as the most available crucial DRM resource,with higher availability of DRM resources correlating positively and significantly with sites’*** findings con-tribute valuable insights to address missing links for disaster-ready and resilient UNESCO sites,promoting their preservation for future generations.

关键词： Biosphere reserves Disaster risk management(DRM) Global geoparks Person-relative-to-event(PRE)fra.ework Sustainability World heritage sites

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Experimental and Numerical Analysis of a PCM-Integrated Roof for Higher Thermal Performance of Buildings

引用

Journal of Thermal Science 2024年第2期33卷 522-536页

作者： SIMON fra.çois RUIZ-VALERO Letzai GIRARD Aymeric GALLEGUILLOS Hector Centro de Desarrollo Urbano Sustentable(CEDEUS) Pontificia Universidad Católica de Chile7500000SantiagoChile Facultad de Ciencias e Ingeniería Pontificia Universidad Católica Madre y Maestra(PUCMM)10103Santo DomingoDominican Republic LMGC IMT Mines AlesUniv MontpellierCNRS30100AlèsFrance Facultad de Ingeniería y Ciencias Universidad Adolfo Ibañez2520000Viña del MarChile Centro de Desarrollo Energético Antofagasta(CDEA) Universidad de Antofagasta1240000AntofagastaChile

Phase change materials(PCMs) designate materials able to store latent *** change state from solid to liquid over a defined temperature *** process is reversible and can be used for thermo-technical *** present paper aims to study the thermal performance of an inorganic eutectic PCM integrated into the rooftop slab of a test room and analyze its potential for building thermal *** experiment is conducted in two test rooms in Antofagasta(Chile) during summer,fall,and *** PCM is integrated into the rooftop of the first test room,while the roof panel of the second room is a sealed air *** work introduces a numerical model,which is built using the finite difference method and used to simulate the rooms' thermal *** thermal simulations of the PCM room are performed for other Chilean locations to evaluate and compare the capability of the PCM panel to store latent heat thermal energy in different *** show that the indoor temperature of the PCM room in Antofagasta varies only 21.1℃±10.6℃,while the one of the air-panel room varies 28.3℃±18.5℃.Under the experiment's conditions,the PCM room's indoor temperature observes smoother diurnal fluctuations,with lower maximum and higher minimum indoor temperatures than that of the air-panel *** simulations in other cities show that the PCM panel has a better thermal performance during winter,as it helps to maintain or increase the room temperature by some degrees to reach comfort *** demonstrates that the implementation of such PCM in the building envelope can effectively reduce space heating and cooling needs,and improve indoor thermal comfort in different climates of Chile.

关键词： phase change material thermal energy storage building space heating and cooling energy efficiency designbuilder

来源：

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Community-led total sanitation(CLTS)implementation in West Mamprusi Municipal Assembly in *** do communities think eleven years on?

引用

Global Health Journal 2024年第2期8卷 67-73页

作者： Elijah Adam emmanuel Badu School of Media Creative and Social InquiryCurtin UniversityBentleyWestern AustraliaAustralia School of Population Health Curtin UniversityBentleyWestern AustraliaAustralia

Objective Access to improved sanitation is a fundamental human right and an important aspect of Public ***,an estimated thousands of people in Ghana especially,the West Mamprusi Municipal Assembly(WMMA)still have no access to adequate toilet *** has brought untold health repercussions to the inhabitants,the community,and the environment at *** address this menace,the community-led total sanitation(CLTS)was *** study aimed to assess communities’perspectives on the implementation of CLTS and to understand the factors influencing its success and *** A mixed-method approach involving sequential qualitative and quantitative methods was employed in this *** for the quantitative study were randomly selected and surveyed using *** qualitative study employed focus group discussion involving purposively sampled participants including assembly members,opinion leaders,and assembly *** The CLTS program in WMMA realized an apparent use of construction and proper use of household latrines leading to a reduction of open defecation free(ODF)and two communities achieving sanitized status in the history of the study area,enabling the training of latrine artisans and natural leaders to facilitate the CLTS expansion and sustainability,improved sanitation and hygiene,strengthened the enforcement of community rules and regulations and many *** The CLTS program has received more widespread acceptance in the study area than the previous government policy of constructing public toilets,which was greeted with massive failures due to poor *** ensure that gains achieved through CLTS implementation are sustained longer,it is recommended that chiefs and opinion leaders should be involved in the CLTS programs to ensure checks and *** entrenchment of bylaws and more education to address enduring myths and misconceptions will sustain the *** in the form

关键词： Community-led total sanitation(CLTS) Community development Ghana Sanitation

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Portal hypertension in patients with nonalcoholic fatty liver disease:Current knowledge and challenges

引用

World Journal of Gastroenterology 2024年第4期30卷 290-307页

作者： Anita Madir Ivica Grgurevic emmanuel A Tsochatzis Massimo Pinzani Department of Gastroenterology Hepatology and Clinical NutritionUniversity Hospital DubravaZagreb 10000Croatia School of Medicine University of ZagrebZagreb 10000Croatia Faculty of Pharmacy and Biochemistry University of ZagrebZagreb 10000Croatia UCL Institute for Liver and Digestive Health Royal Free Hospital and University College LondonLondon NW32PFUnited Kingdom

Portal hypertension(PH)has traditionally been observed as a consequence of significant fibrosis and cirrhosis in advanced non-alcoholic fatty liver disease(NAFLD).However,recent studies have provided evidence that PH may develop in earlier stages of NAFLD,suggesting that there are additional pathogenetic mechanisms at work in addition to liver *** early development of PH in NAFLD is associated with hepatocellular lipid accumulation and ballooning,leading to the compression of liver *** compression and intraluminal obstacles cause mechanical forces such as strain,shear stress and elevated hydrostatic pressure that in turn activate mechanotransduction pathways,resulting in endothelial dysfunction and the development of *** spatial distribution of histological and functional changes in the periportal and perisinusoidal areas of the liver lobule are considered responsible for the pre-sinusoidal component of PH in patients with ***,current diagnostic methods such as hepatic venous pressure gradient(HVPG)measurement tend to underestimate portal pressure(PP)in NAFLD patients,who might decompensate below the HVPG threshold of 10 mmHg,which is traditionally considered the most relevant indicator of clinically significant portal hypertension(CSPH).This creates further challenges in finding a reliable diagnostic method to stratify the prognostic risk in this population of *** theory,the measurement of the portal pressure gradient guided by endoscopic ultrasound might overcome the limitations of HVPG measurement by avoiding the influence of the pre-sinusoidal component,but more investigations are needed to test its clinical utility for this *** and spleen stiffness measurement in combination with platelet count is currently the best-validated non-invasive approach for diagnosing CSPH and varices needing *** change remains the cornerstone of the treatment of PH in NAFLD,together with correcting the comp

关键词： Non-alcoholic fatty liver disease Portal hypertension Mechanotransduction Endothelial dysfunction Hepatic venous pressure gradient

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

引用

Digital Communications and Networks 2024年第2期10卷 369-379页

作者： Héber H.Arcolezi Jean-fra.çois Couchot Bechara Al Bouna Xiaokui Xiao Inria andÉcole Polytechnique(IPP) PalaiseauFrance Femto-ST Institute Univ.Bourg.Franche-ComtéUBFCCNRSBelfortFrance TICKET Lab. Antonine University Hadat-BaabdaBaabdaLebanon School of Computing National University of SingaporeSingaporeSingapore

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)*** to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy ***,when collecting user statistics longitudinally,privacy progressively ***,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under *** tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data *** the known literature uses OUE and SUE for two rounds of sanitization(***),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary ***,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or *** shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

关键词： Local differential privacy Discrete distribution estimation Frequency estimation Multidimensional data Longitudinal studies

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

A mediation system for continuous spatial queries on a unified schema using Apache Spark

引用

Big Earth Data 2024年第1期8卷 115-141页

作者： Thi Thu Trang Ngo fra.çois Pinet David Sarramia Myoung-Ah Kang UniversitéClermont Auvergne ISIMAAubièreFrance UniversitéClermont Auvergne INRAEUR TSCFClermont-FerrandFrance UniversitéClermont Auvergne CNRS/IN2P3LPCClermont-FerrandFrance

Recent advances in big and streaming data systems have enabled real-time analysis of data generated by Internet of Things(IoT)systems and sensors in various *** this context,many applications require integrating data from several heterogeneous sources,either stream or static *** such as Apache Spark are able to integrate and process large datasets from different ***,these fra.eworks are hard to use when the data sources are heterogeneous and *** address this issue,we propose a system based on mediation techniques for integrating stream and static data *** integration process of our system consists of three main steps:configuration,query expression and query *** the configuration step,an administrator designs a mediated schema and defines mapping between the mediated schema and local data *** the query expression step,users express queries using customized SQL grammar on the mediated ***,our system rewrites the query into an optimized Spark application and submits the application to a Spark *** results are continuously returned to *** experiments show that our optimizations can improve query execution time by up to one order of magnitude,making complex streaming and spatial data analysis more accessible.

关键词： Streaming data streaming data integration mediator geospatial data continuous queries

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：